Haus - Stay off the train. Metrolink will have extra officers but that just reduces it from deadly to dangerous. You can park downtown, within 3-5 blocks of Market Street if you get there a few hours early. Just head towards Market, between 18th and Broadway and try to find a spot.
Another option is to park a few miles away at a shopping center or someplace like the Galleria or The Promenade at Brentwood and take an Uber/Lyft to the SLU campus area (or Market & Jefferson) then walk to the parade route. Getting an Uber/Lyft back after the parade will be a challenge. The further you walk away from the crowd, towards wherever you parked the better the odds of getting an Uber/Lyft.
Parking will not be cheap within a mile of the parade route. Just keep that in mind.
It will likely be crowded, even in the rain. Plan on everything you do taking longer than expected. Traffic will be a nightmare within 5 miles of the parade route and the rain will only make that worse. I'm sure I don't have to tell you but keep you're head on a swivel and pay attention to your surroundings. It should be a pretty safe environment but most criminals are criminals of opportunity. They will be down there. Don't be one of their victims...
I'm sure it will be one hell of an experience for you and your son. Enjoy it. Soak it all in!!!
-------------------- "Hunts are best measured by the endurance of the memories they produce..."